Getting down to the Fundamentals of Hydrogen Bonding: Anharmonic Vibrational Frequencies of (HF)2 and (H2O)2 from Ab Initio Electronic Structure Computations

Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.

The strength of the OH-bend/OH-stretch Fermi resonance in small water clusters

A novel Raman jet-spectrometer is used to study the Fermi resonance between the OH bending overtone and OH stretching fundamental in small cyclic water clusters (H2O)n with n = 3, 4, 5. The new setup features a recirculating vacuum system which reduces the gas consumption by 2 to 3 orders of magnitude and enables long-term measurements of very weak Raman signals. Raman spectra measured from highly diluted expansions with unprecedented signal-to-noise ratio are presented and cluster-specific intensity ratios and effective coupling constants are derived using Markov-Chain Monte-Carlo methods, yielding a high probability for an almost "perfect" resonance for the tetramer and pentamer, i.e. a close frequency match of bend overtone and stretch fundamental with intensity ratios close to 1, but a larger coupling constant for the trimer, with best estimates close to W5 ≲ 50 cm-1 < W4 ≲ 60 cm-1 < W3 ≈ 65 cm-1.

The sulfur dioxide-water complex: CCSD(T)/CBS anharmonic vibrational spectroscopy of stacked and hydrogen-bonded dimers

This study examines the structures, energies, and IR vibrational spectra of the sulfur dioxide-water SO2(H2O) complexes by employing coupled cluster theory CCSD(T) with Dunning style correlation consistent type basis sets aug-cc-pV(n+d)Z (n = D, T, Q, 5). Complete basis set (CBS) extrapolations have been carried out to predict binding energies for two isomers of the SO2(H2O) complex: a stacked global minimum (1A) structure and a hydrogen-bonded local minimum (1B) structure. The CCSD(T)/CBS extrapolation predicts an intermolecular S-O distance rS⋯O = 2.827 Å for the stacked isomer, which is in excellent agreement with an experimental measurement of 2.824 Å [K. Matsumura et al., J. Chem. Phys., 91, 5887 (1989)]. The CCSD(T)/CBS binding energy for the stacked dimer 1A and hydrogen-bonded form 1B is De = -4.37 kcal/mol and De = -2.40 kcal/mol, respectively. This study also employs anharmonic VPT2 MP2/aug-cc-pV(n+d)Z level corrections to CCSD(T)/aug-cc-pV(n+d)Z vibrational frequencies in both forms of SO2(H2O). The anharmonic CCSD(T)/aug-cc-pV(Q+d)Z OH stretching frequencies in the stacked structure 1A are 3743 cm-1 (ν3) and 3647 cm-1 (ν1), and these align well with the recorded IR spectroscopic values of 3745 and 3643 cm-1, respectively [C. Wang et al., J. Phys. Chem. Lett., 13, 5654 (2022)]. If we combine CCSD(T)/aug-cc-pV(n+d)Z De values with VPT2 vibrational frequencies, we obtain a new CCSD(T)/aug-cc-pV(Q+d)Z anharmonic dissociation energy D0 = -3.48 kcal/mol for 1A and D0 = -1.74 kcal/mol for 1B. In summary, the results presented here demonstrate that the application of CCSD(T) calculations with aug-cc-pV(n+d)Z basis sets and CBS extrapolations is critical in probing the structure and IR spectroscopic properties of the sulfur dioxide-water complex.

Microhydration of Tertiary Amines: Robust Resonances in Red-Shifted Water

Tertiary amines are strong hydrogen bond acceptors. When a water molecule donates one of the OH groups, its in-phase stretching vibration wavenumber is decreased to such an extent that it comes close to the water bending overtone. This gives rise to anharmonic phenomena such as classical Fermi resonance, resonance with multiple-quantum dark states, or combination transitions with low-frequency intermolecular modes. These effects, which contribute to the spectral breadth of room-temperature hydrogen-bonded amine complexes, are disentangled by Fourier transform infrared spectroscopy in pulsed supersonic slit jet expansions. Monohydrates of the amines quinuclidine, N-methylpyrrolidine, N-methylpiperidine, and dimethylcyclohexylamine exhibit systematic mode coupling signatures. These suggest relatively fast energy flow out of the excited OH stretching fundamental into intra- and intermolecular degrees of freedom of the hydrogen-bonded water molecule. Trimeric complexes are spectroscopically separated from the amine monohydrates.

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

A study of OH···O hydrogen bonds along various isolines in 2-ethyl-1-hexanol. Temperature or pressure - which parameter controls their behavior?

The nature of H-bonding interactions is still far from being understood despite intense experimental and theoretical studies on this subject carried out by the leading research centers. In this paper, by a combination of unique high-pressure infrared, dielectric and volumetric data, the intramolecular dynamics of hydroxyl moieties (which provides direct information about H-bonds) was studied along various isolines, i.e., isotherms, isobars, isochrones, and isochores, in a simple monohydroxy alcohol (2-ethyl-1-hexanol). This allowed us to discover that the temperature controls the intermolecular hydrogen bonds, which then affect the intramolecular dynamics of OH units. Although the role of density fluctuations gets stronger as temperature rises. We also demonstrated a clear connection between the intra- and intermolecular dynamics of the associating liquid at high pressure. The data reported herein open a new perspective to explore this important aspect of the glass transition phenomenon and understand H-bonding interactions at varying thermodynamic conditions.

Transferable Potential Function for Flexible H2O Molecules Based on the Single-Center Multipole Expansion

A potential function is presented for describing a system of flexible H₂O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H₂O)_n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Assessing the Experimental Hydrogen Bonding Energy of the Cyclic Water Dimer Transition State with a Cyclooctatetraene-Based Molecular Balance

We have conducted an experimental and computational study of cyclooctatetraene-1,4/1,6-dimethanol (1,4 and 1,6) as a molecular balance with the goal in mind to determine the otherwise inaccessible hydrogen bonding energy (HBE) of the cyclic water dimer, which constitutes a transition state. The 1,4/1,6 folding equilibrium is governed by an intramolecular hydrogen bond in the folded 1,6-isomer, in which the OH groups adopt a cyclic planar geometry, akin to the structure of the cyclic water dimer transition state. We characterized hydrogen bonding in 1,6 and reference complexes utilizing SAPT2 + (3)δMP2/aug-cc-pVTZ and selected quantum theory of atoms in molecule descriptors at M06-2XD3(0)/ma-def2-TZVPP. Additionally, we computed HBEs at the DLPNO-CCSD(T)/aug-cc-pVQZ level of theory. We find that hydrogen bonding in 1,6 is very similar to the interaction in the C_i symmetric cyclic water dimer TS, both in magnitude and character. We experimentally determined the Gibbs free energy of the folding process (ΔG_eq) in a variety of organic solvents via nuclear magnetic resonance spectroscopy measurements at room temperature. By combining experimentally obtained ΔG_eq values with corrections derived from accurate computational methods, we provide estimates for the HBE of cyclic water dimers and the cyclic water dimer TS, as the most stable cyclic water dimer.

Reduced-dimensional vibrational models of the water dimer

A model based on the finite-basis representation of a vibrational Hamiltonian expressed in internal coordinates is developed. The model relies on a many-mode, low-order expansion of both the kinetic energy operator and the potential energy surface (PES). Polyad truncations and energy ceilings are used to control the size of the vibrational basis to facilitate accurate computations of the OH stretch and HOH bend intramolecular transitions of the water dimer (H₂ ¹⁶O)₂. Advantages and potential pitfalls of the applied approximations are highlighted. The importance of choices related to the treatment of the kinetic energy operator in reduced-dimensional calculations and the accuracy of different water dimer PESs are discussed. A range of different reduced-dimensional computations are performed to investigate the wavenumber shifts in the intramolecular transitions caused by the coupling between the intra- and intermolecular modes. With the use of symmetry, full 12-dimensional vibrational energy levels of the water dimer are calculated, predicting accurately the experimentally observed intramolecular fundamentals. It is found that one can also predict accurate intramolecular transition wavenumbers for the water dimer by combining a set of computationally inexpensive reduced-dimensional calculations, thereby guiding future effective-Hamiltonian treatments.

Monomers of Glycine and Serine Have a Limited Ability to Hydrate in the Atmosphere

The role of atmospheric aerosols on climate change is one of the biggest uncertainties in most global climate models. Organic aerosols have been identified as potential cloud condensation nuclei (CCN), and amino acids are organic molecules that could serve as CCN. Amino acids make up a significant portion of the total organic material in the atmosphere, and herein we present a systematic study of hydration for two of the most common atmospheric amino acids, glycine and serine. We compute DLPNO/CCSD(T)//M08-HX/MG3S thermodynamic properties and atmospheric concentrations of Gly(H₂O)_n and Ser(H₂O)_n, where n = 1-5. We predict that serine-water clusters have higher concentrations at n = 1 and 5, while glycine-water clusters have higher concentrations at n = 2-4. However, both glycine and serine are inferred to exist primarily in their nonhydrated monomer forms in the absence of other species such as sulfuric acid.

Calculating Reliable Gibbs Free Energies for Formation of Gas-Phase Clusters that Are Critical for Atmospheric Chemistry: (H2SO4)3

The effects of atmospheric aerosols on our climate are one of the biggest uncertainties in global climate models. Calculating the pathway for the formation of pre-nucleation clusters that become aerosols is challenging, requiring a comprehensive analysis of configurational space and highly accurate Gibbs free energy calculations. We identified a large set of minimum energy configurations of (H₂SO₄)₃ using a sampling technique based on a genetic algorithm and a stepwise density functional theory (DFT) approach and computed the thermodynamics of formation of these configurations with more accurate wavefunction-based electronic energies computed on the DFT geometries. The DLPNO-CCSD(T) methods always return more positive energies compared to the DFT energies. Within the DLPNO-CCSD(T) methods, extrapolating to the complete basis set limit gives more positive free energies compared to explicitly correlated single-point energies. The CBS extrapolation was shown to be robust as both the 4-5 inverse polynomial and Riemann zeta function schemes were within chemical accuracy of one another.

How to VPT2: Accurate and Intuitive Simulations of CH Stretching Infrared Spectra Using VPT2+K with Large Effective Hamiltonian Resonance Treatments

This article primarily discusses the utility of vibrational perturbation theory for the prediction of X-H stretching vibrations with particular focus on the specific variant, second-order vibrational perturbation theory with resonances (VPT2+K). It is written as a tutorial, reprinting most important formulas and providing numerous simple examples. It discusses the philosophy and practical considerations behind vibrational simulations with VPT2+K, including but not limited to computational method selection, cost-saving approximations, approaches to evaluating intensity, resonance identification, and effective Hamiltonian structure. Particular attention is given to resonance treatments, beginning with simple Fermi dyads and gradually progressing to arbitrarily large polyads that describe both Fermi and Darling-Dennison resonances. VPT2+K combined with large effective Hamiltonians is shown to be a reliable framework for modeling the complicated CH stretching spectra of alkenes. An error is also corrected in the published analytic formula for the VPT2 transition moment between the vibrational ground state and triply excited states.

Potential energy surface and bound states of the H2O-HF complex

We present the first global five-dimensional potential energy surface for the H₂O-HF dimer, a prototypical hydrogen bonded complex. Large scale ab initio calculations were carried out using the explicitly correlated coupled cluster approach with single- and double-excitations together with non-iterative perturbative treatment of triple excitations with the augmented correlation-consistent triple zeta basis sets, in which the water and hydrogen fluoride monomers were frozen at their vibrationally averaged geometries. The ab initio data points were fitted to obtain a global potential energy surface for the complex. The equilibrium geometry of the complex corresponds to the formation of a hydrogen bond with water acting as a proton acceptor and a binding energy of D_e = 3059 cm^-1 (8.75 kcal/mol). The energies and wavefunctions of the lowest bound states of the complex were computed using a variational approach, and the dissociation energies of both ortho-H₂O-HF (D₀ = 2089.4 cm^-1 or 5.97 kcal/mol) and para-H₂O-HF (D₀ = 2079.6 cm^-1 or 5.95 kcal/mol) were obtained. The rotational constant of the complex was found to be in good agreement with the available experimental data.

Competition between Solvent-Solvent and Solvent-Solute Interactions in the Microhydration of the Hexafluorophosphate Anion, PF6-(H2O)n=1,2

This study systematically examines the interactions of the hexafluorophosphate anion (PF₆^-) with one or two solvent water molecules (PF₆^-(H₂O)_n where n = 1, 2). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed on each stationary point using a variety of common density functional theory methods (B3LYP, B3LYP-D3, M06-2X, and ωB97XD) and the MP2 and CCSD(T) ab initio methods with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for P, O, and F; denoted as haTZ). Five new stationary points of PF₆^-(H₂O)₂ have been identified, one of which has an electronic energy of approximately 2 kcal mol^-1 lower than the only other dihydrate structure reported for this system. The CCSD(T) computations also reveal that the detailed interactions between PF₆^- and H₂O can be quite difficult to model reliably, with some methods struggling to correctly characterize stationary points for n = 1 or accurately reproduce the vibrational frequency shifts induced by the formation of the hydrated complex. Although the interactions between the solvent and ionic solute are quite strong (CCSD(T) electronic dissociation energy ≈10 kcal mol^-1 for the monohydrate minimum), the solvent-solvent interactions in the lowest-energy PF₆^-(H₂O)₂ minimum give rise to appreciable cooperative effects not observed in the other dihydrate minima. In addition, this newly identified structure exhibits the largest frequency shifts in the OH stretching vibrations for the waters of hydration (with Δω exceeding -100 cm^-1 relative to the values for an isolated H₂O molecule).

New Molecular-Mechanics Model for Simulations of Hydrogen Fluoride in Chemistry and Biology

Hydrogen fluoride (HF) is the most polar diatomic molecule and one of the simplest molecules capable of hydrogen-bonding. HF deviates from ideality both in the gas phase and in solution and is thus of great interest from a fundamental standpoint. Pure and aqueous HF solutions are broadly used in chemical and industrial processes, despite their high toxicity. HF is a stable species also in some biological conditions, because it does not readily dissociate in water unlike other hydrogen halides; yet, little is known about how HF interacts with biomolecules. Here, we set out to develop a molecular-mechanics model to enable computer simulations of HF in chemical and biological applications. This model is based on a comprehensive high-level ab initio quantum chemical investigation of the structure and energetics of the HF monomer and dimer; (HF)_n clusters, for n = 3-7; various clusters of HF and H₂O; and complexes of HF with analogs of all 20 amino acids and of several commonly occurring lipids, both neutral and ionized. This systematic analysis explains the unique properties of this molecule: for example, that interacting HF molecules favor nonlinear geometries despite being diatomic and that HF is a strong H-bond donor but a poor acceptor. The ab initio data also enables us to calibrate a three-site molecular-mechanics model, with which we investigate the structure and thermodynamic properties of gaseous, liquid, and supercritical HF in a wide range of temperatures and pressures; the solvation structure of HF in water and of H₂O in liquid HF; and the free diffusion of HF across a lipid bilayer, a key process underlying the high cytotoxicity of HF. Despite its inherent simplifications, the model presented significantly improves upon previous efforts to capture the properties of pure and aqueous HF fluids by molecular-mechanics methods and to our knowledge constitutes the first parameter set calibrated for biomolecular simulations.

Shifting formic acid dimers into perspective: vibrational scrutiny in helium nanodroplets

A metastable dimer of formic acid has been prepared inside superfluid helium nanodroplets and examined using IR spectroscopy and quantum chemical calculations.

Temperature Dependence of Intramolecular Vibrational Bands in Small Water Clusters

Cyclic water clusters are pivotal for understanding atmospheric reactions as well as liquid water, yet the temperature (T) dependence of their dynamics and spectroscopy is poorly studied. The development of highly accurate water potentials, such as MB-pol, partly rectifies this. It remains to account for the quantum nuclear effects (NQE), because quantum nuclear dynamics become increasingly inaccurate at low temperatures. From a practical point of view, we find that NQE can be accounted for simply by subtracting a constant from the frequencies obtained from the velocity autocorrelation functions (VACF) of classical nuclear dynamics, resulting in unprecedented agreement with experiment, mostly within 5 cm^-1. We have performed classical simulations of (H₂O)_n clusters (n = 2-5) from 20 K and up to their melting temperature, calculating both all-atom and partial VACF, thus generating the temperature dependence of the vibrational frequencies (IR and Raman bands). Focusing on the hydrogen-bonded (HBed) OH stretch and HOH bend, we find opposing T dependencies. The HBed OH modes blue shift linearly with T, attributed to ring expansion rather than any specific conformational change. The lowest-frequency Raman concerted mode is predicted to show the largest such shift. In contrast, the HOH bend undergoes a red-shift, with the highest frequency concerted band undergoing the largest red-shift. These results can be explained by a coupled-oscillator model for n hydrogen atoms on a ring, constrained to move either tangentially (stretch) or perpendicularly (bend) to the ring. With increasing temperature and weakening of HBs, the intrinsic force constant increases (stretch) or remains constant (bend), while the nearest-neighbor coupling constant decreases, and this results in the interesting behavior revealed herein. T-dependent Raman studies are required for testing some of these predictions.

Performance of polarization-consistent vs. correlation-consistent basis sets for CCSD(T) prediction of water dimer interaction energy

Detailed study of Jensen’s polarization-consistent vs. Dunning’s correlation-consistent basis set families performance on the extrapolation of raw and counterpoise-corrected interaction energies of water dimer using coupled cluster with single, double, and perturbative correction for connected triple excitations (CCSD(T)) in the complete basis set (CBS) limit are reported. Both 3-parameter exponential and 2-parameter inverse-power fits vs. the cardinal number of basis set, as well as the number of basis functions were analyzed and compared with one of the most extensive CCSD(T) results reported recently. The obtained results for both Jensen- and Dunning-type basis sets underestimate raw interaction energy by less than 0.136 kcal/mol with respect to the reference value of − 4.98065 kcal/mol. The use of counterpoise correction further improves (closer to the reference value) interaction energy. Asymptotic convergence of 3-parameter fitted interaction energy with respect to both cardinal number of basis set and the number of basis functions are closer to the reference value at the CBS limit than other fitting approaches considered here. Separate fits of Hartree-Fock and correlation interaction energy with 3-parameter formula additionally improved the results, and the smallest CBS deviation from the reference value is about 0.001 kcal/mol (underestimated) for CCSD(T)/aug-cc-pVXZ calculations. However, Jensen’s basis set underestimates such value to 0.012 kcal/mol. No improvement was observed for using the number of basis functions instead of cardinal number for fitting.

Soft experimental constraints for soft interactions: a spectroscopic benchmark data set for weak and strong hydrogen bonds

An experimental benchmark data base on rotational constants, vibrational properties and energy differences for weakly and more strongly hydrogen-bonded complexes and their constituents from the spectroscopic literature is assembled. It is characterized in detail and finally contracted to a more compact, discriminatory set (ENCH-51, for Experimental Non-Covalent Harmonic with 51 entries). The meeting points between theory and experiment consist of equilibrium rotational constants and harmonic frequencies and energies, which are back-corrected from experimental observables and are very easily accessible by quantum chemical calculations. The relative performance of B3LYP-D3, PBE0-D3 and M06-2X density functional theory predictions with a quadruple-zeta basis set is used to illustrate systematic errors, error compensation and selective performance for structural, vibrational and energetical observables. The current focus is on perspectives and different benchmarking methodologies, rather than on a specific theoretical method or a specific class of compounds. Extension of the data base in chemical, observable and quantum chemical method space is encouraged.

Cis/Trans Energetics in Epoxide, Thiirane, Aziridine and Phosphirane Containing Cyclopentanols: Effects of Intramolecular OH⋯O, S, N and P Contacts

A recent computational analysis of the stabilizing intramolecular OH⋯O contact in 1,2-dialkyl-2,3-epoxycyclopentanol diastereomers has been extended to thiiriane, aziridine and phosphirane analogues. Density functional theory (DFT), second-order Møller-Plesset perturbation theory (MP2) and CCSD(T) coupled-cluster computations with simple methyl and ethyl substituents indicate that electronic energies of the cis isomers are lowered by roughly 3 to 4 kcal mol⁻¹ when the OH group of these cyclopentanol systems forms an intramolecular contact with the O, S, N or P atom on the adjacent carbon. The results also suggest that S and P can participate in these stabilizing intramolecular interactions as effectively as O and N in constrained molecular environments. The stabilizing intramolecular OH⋯O, OH⋯S, OH⋯N and OH⋯P contacts also increase the covalent OH bond length and significantly decrease the OH stretching vibrational frequency in every system with shifts typically on the order of −41 cm⁻¹.

Anharmonicity of Vibrational Modes in Hydrogen Chloride-Water Mixtures

A thorough analysis of molecular vibrations in the binary system hydrogen chloride/water is presented considering a set of small mixed and pure clusters. In addition to the conventional normal-mode analysis based on the diagonalization of the Hessian, anharmonic frequencies were obtained from the perturbative VPT2 and PT2-VSCF method using hybrid density functional theory. For all normal modes, potential energy curves were modeled by displacing the atoms from the minimum geometry along the normal mode vectors. Three model potentials, a harmonic potential, a Morse potential, and a fourth order polynomial, were applied to fit these curves. From these data, it was possible not only to characterize distinct vibrations as mainly harmonic, anharmonic, or involving higher order terms but also to extract force constants, k, and anharmonicity constants, x_e. By investigating all different types of intramolecular vibrations including covalent stretching or bending vibrations and intermolecular vibrations such as librations, we could demonstrate that while vibrational frequencies can be obtained applying scaling factors to harmonic results, useful anharmonicity constants cannot be predicted in such a way and the usage of more elaborate vibrational methods is necessary. For each particular type of molecular vibration, we could however determine a relationship between the wavenumber or wavenumber shift and the anharmonicity constant, which allows us to estimate mode dependent anharmonicity constants for larger clusters in the future.

Effect of Electron Correlation on Intermolecular Interactions: A Pair Natural Orbitals Coupled Cluster Based Local Energy Decomposition Study

The development of post-Hartree-Fock (post-HF) energy decomposition schemes that are able to decompose the HF and correlation components of the interaction energy into chemically meaningful contributions is a very active field of research. One of the challenges is to provide a clear-cut quantification to the elusive London dispersion component of the intermolecular interaction. London dispersion is well-known to be a pure correlation effect, and as such it is not properly described by mean field theories. In this context, we have recently developed the local energy decomposition (LED) analysis, which provides a chemically meaningful decomposition of the interaction energy between two or more fragments computed at the domain-based local pair natural orbitals coupled cluster (DLPNO-CCSD(T)) level of theory. In this work, this scheme is used in conjunction with other interpretation tools to study a series of molecular adducts held together by intermolecular interactions of different natures. The HF and correlation components of the interaction energy are thus decomposed into a series of chemically meaningful contributions. Emphasis is placed on discussing the physical effects associated with the inclusion of electron correlation. It is found that four distinct physical effects can contribute to the magnitude of the correlation part of intermolecular binding energies (Δ E_int^C): (i) London dispersion, (ii) the correlation correction to the reference induction energy, (iii) the correlation correction to the electron sharing process, and (iv) the correlation correction to the permanent electrostatics. As expected, the largest contribution to the correlation binding energy of neutral, apolar molecules is London dispersion, as in the argon dimer case. In contrast, the correction for the HF induction energy dominates Δ E_int^C in systems in which an apolar molecule interacts with charged or strongly polar species, as in Ar-Li⁺. This effect has its origin in the systematic underestimation of polarizabilities at the HF level of theory. For similar reasons, electron sharing largely contributes to the correlation binding energy of covalently bound molecules, as in the beryllium dimer case. Finally, the correction for HF permanent electrostatics significantly contributes to Δ E_int^C in molecules with strong dipoles, such as water and hydrogen fluoride dimers. This effect originates from the characteristic overestimation of dipole moments at the HF level of theory, leading in some cases to positive Δ E_int^C values. Our results are apparently in contrast to the widely accepted view that Δ E_int^C is typically dominated by London dispersion, at least, in the strongly interacting region. Clearly, post-HF energy decomposition schemes are very powerful tools to analyze, categorize, and understand the various contributions to the intermolecular interaction energy. Hopefully, this will eventually lead to insights that are helpful in designing systems with tailored properties. All analysis tools presented in this work will be available free of charge in the next release of the ORCA program package.

Dissociation Energy of the H2O···HF Dimer

Even though (H₂O)₂ and (HF)₂ are arguably the most thoroughly characterized prototypes for hydrogen bonding, their heterogeneous analogue H₂O···HF has received relatively little attention. Here we report that the experimental dissociation energy ( D₀) of this important paradigm for heterogeneous hydrogen bonding is too large by 2 kcal mol^-1 or 30% relative to our computed value of 6.3 kcal mol^-1. For reference, computational procedures similar to those employed here to compute D₀ (large basis set CCSD(T) computations with anharmonic corrections from second-order vibrational perturbation theory) provide results within 0.1 kcal mol^-1 of the experimental values for (H₂O)₂ and (HF)₂. Near the CCSD(T) complete basis set limit, the electronic dissociation energy for H₂O···HF is ∼4 kcal mol^-1 larger than those for (H₂O)₂ and (HF)₂ (∼9 kcal mol^-1 for the heterogeneous dimer vs ∼5 kcal mol^-1 for the homogeneous dimers). Results reported here from symmetry-adapted perturbation theory computations suggest that this large difference is primarily due to the induction contribution to the interaction energy.

Local energy decomposition analysis of hydrogen-bonded dimers within a domain-based pair natural orbital coupled cluster study

The local energy decomposition (LED) analysis allows for a decomposition of the accurate domain-based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] energy into physically meaningful contributions including geometric and electronic preparation, electrostatic interaction, interfragment exchange, dynamic charge polarization, and London dispersion terms. Herein, this technique is employed in the study of hydrogen-bonding interactions in a series of conformers of water and hydrogen fluoride dimers. Initially, DLPNO-CCSD(T) dissociation energies for the most stable conformers are computed and compared with available experimental data. Afterwards, the decay of the LED terms with the intermolecular distance (r) is discussed and results are compared with the ones obtained from the popular symmetry adapted perturbation theory (SAPT). It is found that, as expected, electrostatic contributions slowly decay for increasing r and dominate the interaction energies in the long range. London dispersion contributions decay as expected, as r-6. They significantly affect the depths of the potential wells. The interfragment exchange provides a further stabilizing contribution that decays exponentially with the intermolecular distance. This information is used to rationalize the trend of stability of various conformers of the water and hydrogen fluoride dimers.

Neutral and anionic phosphate-diesters as molecular templates for the encapsulation of a water dimer

Neutral and anionic phosphate diesters act as molecular templates for the encapsulation of water dimers.

The water dimer reaction OH + (H2O)2 → (H2O)-OH + H2O

The stationary points, including the entrance complex, transition states, and the exit complex, for the reaction OH + (H₂O)₂ → (H₂O)OH + H₂O have been carefully examined using the "gold standard" CCSD(T) method with the correlation-consistent basis sets up to cc-pVQZ. The complex (H₂O)₂OH is found to lie 10.8 kcal mol^-1 below the separated reactants. This complex should be observable in the gas phase via vibrational or microwave spectroscopy. Seven unique transition states were found. One pathway for the title reaction has no barrier, in which the OH radical captures a whole water molecule from the water dimer. For the hydrogen abstraction pathways the lowest classical barrier height is predicted to be 5.9 kcal mol^-1 (TS1) relative to separated reactants, and the other pathways are of higher barriers, i.e., 17.8 (TS2) and 18.4 (TS3) kcal mol^-1. The harmonic vibrational frequencies and the zero-point vibrational energies of the stationary points for the reaction are also reported.

Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?

Theoreticians and experimentalists should work together more closely to establish reliable rankings and benchmarks for quantum chemical methods. Comparison to carefully designed experimental benchmark data should be a priority. Guidelines to improve the situation for experiments and calculations are proposed.

Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions

Almost 50 years have passed from the first computer simulations of water, and a large number of molecular models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of analytical potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approximations and on their ability to accurately reproduce reference data obtained from state-of-the-art electronic structure calculations and experimental measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a physically correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought "universal model" capable of describing the behavior of water under different conditions and in different environments.

Challenging Dogmas: Hydrogen Bond Revisited

Hydrogen bond directionality in the water dimer is explained on the basis of symmetry-adapted intermolecular perturbation theory which directly separates the intermolecular interaction energy into four physically interpretable components: electrostatics, exchange-repulsion, dispersion, and induction. Analysis of these four main contributions to the binding energy allows a deeper understanding of the dominant factors ruling the mutual arrangement of the two monomers. A preference for the linear configuration is shown to be due to a subtle interplay of all four energy components. While the first-order terms, electrostatic and exchange-repulsion, almost perfectly cancel each other near the equilibrium geometry of the dimer, the importance of the second- and higher-order terms, induction and dispersion, becomes evident.

Assessing the accuracy of some popular DFT methods for computing harmonic vibrational frequencies of water clusters

A wide range of density functional theory (DFT) methods (37 altogether), including pure, hybrid, range-separated hybrid, double-hybrid, and dispersion-corrected functionals, have been employed to compute the harmonic vibrational frequencies of eight small water clusters ranging in size from the dimer to four different isomers of the hexamer. These computed harmonic frequencies have been carefully compared to recently published benchmark values that are expected to be very close to the CCSD(T) complete basis set limit. Of the DFT methods examined here, ωB97 and ωB97X are the most consistently accurate, deviating from the reference values by less than 20 cm(-1) on average and never more than 60 cm(-1). The performance of double-hybrid methods including B2PLYP and mPW2-PLYP is only slightly better than more economical approaches, such as the M06-L pure functional and the M06-2X hybrid functional. Additionally, dispersion corrections offer very little improvement in computed frequencies.

Low Temperature Kinetics of the First Steps of Water Cluster Formation

We present a combined experimental and theoretical low temperature kinetic study of water cluster formation. Water cluster growth takes place in low temperature (23-69 K) supersonic flows. The observed kinetics of formation of water clusters are reproduced with a kinetic model based on theoretical predictions for the first steps of clusterization. The temperature- and pressure-dependent association and dissociation rate coefficients are predicted with an ab initio transition state theory based master equation approach over a wide range of temperatures (20-100 K) and pressures (10^{-6}-10  bar).